Three dimensional mapping

ABSTRACT

Methods and apparatus are provided for locating the position, preferably in three dimensions, of a sensor by generating magnetic fields which are detected at the sensor. The magnetic fields are generated from a plurality of locations and, in one embodiment of the invention, enable both the orientation and location of a single coils sensor to be determined. The present invention thus finds application in many areas where the use of prior art sensors comprising two or more mutually perpendicular coils is inappropriate.

This application is a division of Ser. No. 09/336,723 filed Jun. 21,1999, now abandoned, which is a division of Ser. No. 08/392,955 filedMay 30, 1995, now U.S. Pat. No. 5,913,820, which is a 371 ofPCT/GB93/01736 filed Aug. 16, 1993.

FIELD OF THE INVENTION

The present invention relates to methods of and apparatus for,determining the location of an object and in particular, but notexclusively to methods and apparatus which employ a magnetic field whichis sensed at the object.

BACKGROUND OF THE INVENTION

It has been long appreciated that if the magnetic field around a fieldgenerating element, for example, a generating coil, can be accuratelymapped than it might be possible to determine the location of a fieldssensor, for example a sensing coil, relative to the generating coil,from the signals sensed by such a sensing coil. However, a problemassociated with doing this is that there are in general many locationsand/or orientations of the sensing coil within the field of thegenerating coil that will provide the same characteristic sensingsignals in the sensing coil. In order to use a magnetic field for thispurpose, additional information must therefore be provided.

Prior art approaches to providing the additional information requiredcomprise either moving the generating and sensing coils relative to eachother, or scanning the axis of the generated field past the sensingcoil.

An example of the first approach is taught in U.S. Pat. No. 3,644,825wherein a system is disclosed for locating the position of a fieldsensor, comprising two orthogonal sensing coils, relative to a fieldgenerating element which relies on having knowledge of the direction ofmotion of the sensor relative to the generator. It should be noted thatthis system cannot detect the location of an object unless there is suchrelative motion, and its direction is known.

The second approach of scanning the axis of the generated field isdisclosed, for position location in two dimensions, in U.S. Pat. No.3,121,228 and for position location in three dimensions in U.S. Pat. No.3,868,565.

U.S. Pat. No. 3,121,228 describes how the distance and direction of asensor, again comprising two orthogonal sensing coils, relative to afield generator, also comprising two orthogonal coils, can bedetermined. The two orthogonal generating coils are driven in phasequadrature so that the axis of the resultant field is caused to rotatewithin a plane. If the sensor is located within this plane then the axisof the field is guaranteed to scan part the sensor, and, because at anygiven distance from a field generator the field strength will be amaximum at the field axis, the sensor will detect a maximum in fieldstrength at this time. The voltage induced in any one of the two coilsforming the sensor will be dependent on the orientation of the coilrelative to the field generator, and it is for this reason that is '228two orthogonal coils are utilised in the sensor. The sum of these twovoltages gives an indication of the distance between the sensor andgenerator, while the phase difference between the two voltages gives anindication of the direction of the generator relative to the sensor. Itis thus essential to the operation of the location system of '228 thatthe axis of the field rotates and that two coils are present in thesensor.

In U.S. Pat. No. 3,868,565 this approach of scanning the axis, ormaximum intensity vector, of the field part the sensor is extended toallow location of the sensor in three dimensions. Whereas in twodimensions it is sufficient merely to rotate the axis of the fieldwithin the plane to be sensed to guarantee it passing through thesensor, in three dimensions the axis would have to be rotated so that itdescribed the surface of a sphere in order to be certain it encounteredthe sensor. To ensure that the axis passed through all points on thesurface of a sphere the motion of the axis would be such that itencountered the sensor only very infrequently, and thus measurements bythe sensor of the maximum field strength would also be infrequent. Toavoid this the location system of '565 drives the generator coils in acomplex fashion so that the field axis tracks and rotates around theposition of the sensor.

In order to locate the position of the sensor in three dimensions,according to the method of '565, three mutually orthogonal generatingcoils and three mutually orthogonal sensing coils are required and thethree generating coils must be driven simultaneously by the three drivecurrents having amplitude and phase relationships between them which arecontrolled so as to direct the field axis towards the sensor.

The approach taken in '565 further requires that the various equationsgoverning the voltage induced in a sensing coil located and orientatedin a particular alternating magnetic field are solved dynamically inreal time ie. during the acquisition of data from the sensing coil. Thisrequirement, in addition to limiting the speed at which the sensor canmove while still being located successfully by the system, also meansthat should it be desired to locate more than one sensor, all apparatuswill need to be duplicated for each additional sensor.

U.S. Pat. No. 4,710,708 discloses a position location system, in whichit is not necessary to scan the field axis. '708 employs multiple coilfield generators and a single coil sensor, but utilises standarditerative algorithms to solve for all the variables of the relevantsimultaneous equations, in a computationally intensive manner.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided amethod of determining the location and the orientation of a field sensorrelative to a plurality of field generators of known location, eachfield generator comprising a plurality of collocated field generatingelements, the method comprising the steps of:

1) for each generator, energising each generating element and measuringthe respective field generated by each generating element at the fieldsensor,

2) for each field generator calculating, from the measurements of thefield generated by each of its generating elements, and in estimate ofthe orientation of the sensor an estimate of the distance from thatparticular field generator to the sensor,

3) utilising the estimates of the distances from each of the fieldgenerators to the sensor, and the known location of the field generatorsto calculate the location of the sensor relative to the fieldgenerators,

4) employing the estimated location of the sensor from step 3) and themeasurements of the field at the sensor to calculate a new estimate ofthe orientation of the sensor, and

5) repeating steps 2) to 4)iteratively, with step 2) employing the newestimate of sensor orientation from the preceding step 4), to improvethe estimates of location and orientation of the sensor.

The method of the first aspect of the present invention thus enables thelocation of a sensor to be determined without either relative motionbetween the sensor and the field generating element, or scanning of theaxis of the field.

Furthermore, by calculating an estimate of the distance of the sensorfrom each field generator, a surprisingly accurate estimate of theposition of the sensor is achieved in a computationally simple manner.

Since the method dissociates the stages of acquisition of data from thesensor, and processing of that data, rapid determination of the sensorlocation is facilitated. Furthermore the location of additional sensorsmay be determined simply by simultaneous measuring the field, generatedby each generating element, at these other sensors and independentlycalculating their distances from the field generators. It should benoted that no modification of the field generating apparatus or methodof driving the apparatus is required in order to determine the locationof a plurality of sensors.

The applicants have discovered that advantageously the method of thefirst aspect of the present invention also allows the location of asensor comprising a single sensing element, for example a sensing coil,to be determined, as will be explained subsequently. This isparticularly advantageous for positioning applications in which two ormore mutually orthogonal sensing coils, as required by prior arttechniques, cannot be used.

According to a second aspect of the present invention there is provideda method of determining the location of a field sensor, comprising aplurality of collocated field sensing elements, relative to a fieldgenerator, comprising a plurality of collocated field generatingelements, the method comprising the steps of:

1) energising a single field generating element to establish a field,

2) measuring a value of the field strength at the field sensor which isdependent on the location and orientation of the sensor within thefield,

3) repeating steps 1) and 2) for each field generating element,

4) calculating, by utilising all the values measured in step 2 and anestimate of the direction of the sensor from the field generator, adirection dependent weighting factor for each field generating elementso that the calculated field strength B is equal to the field strength Bthat would exist at the sensor if the axis of the field were directedtowards the sensor.

5) iteratively altering the direction dependent weighting factors tomaximise B and thus to determine to a desired level of accuracy thedirection of the sensor from the field generator, and

6) employing the measured values of the field strength to calculate thedistance of the sensor from the field generator and hence, from thedirection of the sensor in step 5), the location of the sensor relativeto the field generator.

This aspect of the invention thus provides a method of locating a sensorrelative to a single field generator.

The invention further provides apparatus suitable for carrying out themethods of the first two aspects of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the present invention will now be described, byway of example only, with reference to the accompanying figures inwhich:

FIG. 1 shows a first embodiment of the invention,

FIG. 2 shows the cartesian coordinate system employed for a sensor ofarbitrary orientation located at point P,

FIG. 3 shows schematically the resolution of the magnetic flux densityat a sensor,

FIG. 4 shows the coordinate system employed to locate a sensor relativeto a field generator,

FIG. 5 shows schematically a simulated circle of constant inducedvoltage, in a sensor, in two dimensions, which is employed in the firstembodiment of the invention

FIG. 6 shows schematically three simulated spheres of constant inducedvoltage each centred on a field generator, which is employed in thefirst embodiment of the invention,

FIG. 7 shows a flow chart of a first positioning algorithm used in thefirst embodiment of the invention,

FIG. 8 shows the same schematic as FIG. 6 when the location andorientation of the sensor have been determined,

FIGS. 9, 10 and 11 schematically show a coordinate system employed in asecond positioning algorithm used in the first embodiment of theinvention,

FIGS. 12(a) to 12(f) show images of an endoscope obtained using thepositioning systems of the present invention on the left, and imagesobtained conventionally using X-rays on the right, 12(a) and (b) show asigmoid loop, 12(c) and (d) show an alpha loop, and 12(e) and (f) show areverse alpha loop,

FIGS. 13(a) to 13(d) show images of an endoscope within a patientobtained using the present positioning system on the left, and obtainedusing conventional X-ray imaging on the right, 13(a) and (b) show ananterior view, and 13(c) and (d) show a lateral view.

FIG. 14 shows a second embodiment of the invention,

FIG. 15 is an illustration of a data glove having one or more sensorcoils attached to fingers of the glove.

FIG. 16 depicts resolving magnetic flux density at a distance.

FIG. 17 depicts resolving magnetic flux density onto an x-y-z Cartesiancoordinate system.

FIG. 18 depicts resolving the magnetic flux density at P onto the x-yplane.

In a first embodiment the invention enables a sensor comprising a singlesensing coil to be located in three dimensions relative to a planedefined by three field generators.

DETAILED DESCRIPTION OF THE DRAWINGS

With reference to FIG. 1, three field generators 1 are mounted at knownlocations on a plane surface 2. Each field generator 1 comprises threeelectrically separate coils of wire (generating coils) 3 wound about acuboid wooden former 4, which is approximately 40 mm along one side. Thethree coils of each field generator are wound so that the axes of thecoils are mutually perpendicular. The nine generating coils areseparately electrically connected to an amplifier 5 which is able, underthe direction of a controller 6, to drive each of the coilsindividually. Each coil comprises 40 turns of 0.45 mm copper wire andhas an inductance of approximately 75 μH.

The sensor 7 comprises a single sensing coil of 200 turns of 42 swg wireon a ferrite core of diameter 0.8 mm, and length 12 mm. Larger sensorcoils will in general by more sensitive to the electro-magnetic fieldsgenerated by the generating coils, however the size of the coil isnormally governed by the particular position location problem which isbeing addressed and frequently small sensor coils will be required. Foran air-cored coil the sensitivity of the sensor depends on the area ofthe coil, however the sensitivity can be increased by utilising a highmagnetic permeability material in the core, and in this case thesensitivity will depend more strongly on the length of the coil then onits diameter. The sensing coil is electrically connected to ameasurement unit 8 which in turn is connected to the controller 6. Themeasurement unit 8 comprises an analogue to digital converter, and amatched filter (not shown).

In use, the controller 6 directs the amplifier 5 to drive each of thenine generating coils 3 sequentially. The amplifier 5 outputs a 10 kHzdrive signal of 3 amps rms which causes the particular generating coilhaving driven to generate a quasi-static magnetic field. The frequencyof the drive signal is chosen so that, within the range over which thelocation of the sensor is to be determined, the field generated is anear-field electro-magnetic field i. e the wavelength is long comparedto the distance from the generating coil to the sensing coil.

Furthermore the drive signal frequency must be chosen so as to provide acompromise between sensor coil sensitivity, and the detrimental effectsof electro-magnetic noise due to induced eddy currents withinelectrically conductive objects within the positioning range, since bothof these aspects increase with frequency. In the absence of electricallyconducting objects a frequency of several hundred kilohertz may be usedgiving good sensor sensitivity and thus good range and positioningaccuracy. In the presence of highly conductive objects, this frequencymay need to be reduced to a few hertz. In this case a sensor coil may nolonger be appropriate and may be replaced by an alternative magneticfield sensor, such as a flux gate magnetometer. In this embodiment adrive frequency of 10 kHz has been found to be a suitable compromisebetween sensitivity and immunity to interference from electricallyconductive objects.

Once the quasi-static field from a particular generating coil 3 isestablished, the value of the voltage induced in the sensing coil 7 bythis field is measured by the measurement unit 8. The signal from thesensing coil 7 is first amplified and then sampled at 40 kHz by a 16 bitanalogue-to-digital converter. The sampled signal is windowed using aBlackman-Harris window, the 10 kHz component is extracted by the matchedfilter and hence a value representing the voltage induced in the sensingcoil 7 is established. This value is passed to the controller 6 whichstores the value and then instructs the amplifier 5 to stop driving thepresent generating coil 3 and to start driving the next generating coil3. When all nine generating coils 3 have been driven, or energised, andthe corresponding nine voltages induced in the sensing coil 7 have beenmeasured and stored, the controller 6 calculates the location andorientation of the sensor 7 relative to the field generators 1 anddisplays this on a display device 9. This calculation can be carried outwhile the subsequent set of nine measurements are being taken. Thus, bysequentially driving each of nine generating coils 3, arranged in threegroups of three mutually orthogonal coils, the location and orientationof a single sensing coil 7 can be determined.

In order to describe the algorithm employed by the controller 6 tocalculate the location and orientation of the sensor 7, a coordinatesystem will first be defined. In FIG. 2 is shown a sensor, located atposition P, whose axis is orientated along direction S. In general inorder to determine the location and orientation of a single sensing coilwithin a field the x, y, z cartesian coordinates of the sensor and theelevation angle θ, and rotational angle φ, must be found (see FIG. 2).The vector distance R of the sensor from the origin, O, of thecoordinate system is also shown in FIG. 2. Both the location andorientation of the sensing coil within the field will affect the voltageinduced in the coil by the field, but rotation of the coil about itsaxis will not affect the induced voltage and thus does not constitute afurther unknown quantity.

Assuming now that a single field generating coil 3 is placed at theorigin O of the coordinate system with its axis directed along thez-axis. When the generating coil is energised a field will be producedat the sensor location P which has a magnetic flux density B. Withreference to FIG. 3 this magnetic flux B can be resolved along the threeaxes of the coordinate system to give Bx, By and Bz and subsequentlyresolved along the axis of the sensor thus:

B _(xy) =B _(x) cosφ+B _(y) sinφ  (1)

and

B _(s) =B _(z) cosθ+B _(xy) sinθ  (2)

The voltage V₁, induced in the sensor is related to the flux density viaV_(s)=k_(s) B_(z) where k_(s) is known and is a function of thefrequency of the field and the characteristic of the sensing coil. Ittherefore follows from (1) and (2) that the voltage induced in thesensor at any x-y-z location and for any θ−φ orientation is given by,

V _(s) =k _(s)(B _(z) cosθ−sinθ(B _(x) cosφ+B _(y) sinφ))   (3)

Formulae defining B_(x), B_(y) and B_(z) are developed from standardnear field electromagnetic theory. Upon substituting the terms forB_(x), B_(y), B_(z) from equation (A-12) to (A-14) into (3), it can beshown that, $\begin{matrix}{V_{s} = {k_{c}\quad {k_{s}\lbrack \frac{{( {{2z^{2}} - x^{2} - y^{2}} )\quad \cos \quad \theta} + {3z\quad \sin \quad \theta \quad ( {{x\quad \cos \quad \varphi} + {y\quad \sin \quad \varphi}} )}}{( {x^{2} + y^{2} + z^{2}} )^{5\text{/}2}} \rbrack}}} & (4)\end{matrix}$

where k_(c) is shown and is a function of the current through, diameterof, and number of turns on the generating coil. The five unknownquantities, x, y, z, θ and φ are evident in (4): all other variables areknown.

Equation (4) has been derived, as stated above, for the case of a singlegenerating coil 3 directed along the z-axis, there will of course be acorresponding equation for each of the three generating coils 3 of eachof the three field generators 1.

It has been found that despite the complexity of this term (4) it ispossible to determine the location and orientation of a single sensingcoil by sequentially energising each generating coil. To explain thisapproach to position location the two dimensional case will first beconsidered.

FIG. 4 shows a field generator comprising two orthogonal fieldgenerating coils D_(x) and D_(y) located at the origin of the coordinatesystem. The single sensing coil sensor is located at P and its axis isparallel to direction S. The angle α is the angle between vectordirection R of the sensor from the origin, and the direction S of thesensor axis.

The voltages induced in the sensor when coils D_(x) and D_(y) areenergised sequentially are respectively,

V _(sDx) =k _(s)(B _(RDX) cosα−B _(θDx) sinα)   (5)

and

V _(sDy) =k _(s)(B _(RDy) cosα+B _(θDy) sinα)   (6)

where the D_(x) and D_(y) sub-suffices relate to the field generated bythe D_(x) and D_(y) coils. Upon substituting (A-1) and (A-2) (5) and (6)become,

V _(sDx) K _(c) k _(s) /R ³ (2 cosθcosα−sinθsinα)   (7)

V _(sDy) k _(c) k _(s) /R ³ (2 sinθcosα+cosθsinα)   (8)

It has been noticed that the value of {square root over (V_(sDx)²+V_(sDy) ²)} remains constant for a constant value of α.

From (7) and (8) we can write. $\begin{matrix}{\sqrt{V_{s0x}^{-} - V_{s0y}^{2}} = {\frac{k_{c}\quad k_{s}}{R^{3}}\begin{bmatrix}{{4\quad \cos^{2}\quad \theta \quad \cos^{2}\quad \alpha} + {\sin^{2}\quad \theta \quad \sin^{2}\quad \alpha} -} \\{{4\quad \sin \quad \theta \quad \sin \quad \alpha \quad \cos \quad \theta \quad \cos \quad \alpha} +} \\{{4\quad \sin^{2}\quad \theta \quad \cos^{2}\quad \alpha} + {\cos^{2}\quad \theta \quad \sin^{2}\quad \alpha} +} \\{4\quad \sin \quad \theta \quad \cos \quad \alpha \quad \cos \quad \theta \quad \sin \quad \alpha}\end{bmatrix}}} & (9)\end{matrix}$

which reduces to: $\begin{matrix}{\sqrt{V_{s0x}^{2} + V_{s0y}^{2}} = {\frac{k_{c}\quad k_{s}}{R^{3}}\quad \sqrt{1 + {3\quad \cos^{2}\quad \alpha}}}} & (10)\end{matrix}$

This can be thought of as corresponding physically to a circle ofconstant induced voltage in the sensor, centred on the field generatorat the origin and lying in the x-y plane. This concept is shownschematically in FIG. 5. If the two individual measurements of inducedvoltage V_(sDx) and V_(sDy) measured at the sensor are used to calculate{square root over (V_(sDx) ²+V_(sDy) ²)} a circular or rotating field ofconstant strength can be simulated since {square root over (V_(sDx)²+V_(sDy) ²)} represents the maximum voltage that could be induced inthe sensor if a rotating field were used. This is desirable sinceequation 10 gives a very simple relationship between R and α.

The extension of this analysis to three dimensions is readily performedmathematically and conceptually very powerful because the approach takendoes not require the axis of the generated field to be steered towardsthe sensor, but simply requires sequential energising of the individualgenerating coils. Thus for position determination in three dimensions ofa single coil sensor, assuming three mutually perpendicular generatingcoils located at the origin of the coordinate system, we have$\begin{matrix}{\sqrt{V_{s0x}^{2} + V_{s0y}^{2} + V_{s0z}^{2}} = {\frac{k_{c}\quad k_{s}}{R^{3}}\quad \sqrt{1 + {3\quad \cos^{2}\quad \alpha}}}} & (11)\end{matrix}$

It should be noted that the term {square root over (1+3 cos²α)} can onlytake values between 1 and 2, ignoring negative solutions and thus anyvalue of R computed from (11) is only weakly dependent on the value ofα. For example, if α is assumed to be π/2 whereas its correct value iszero, the value of R computer from (11) is 80% of its correct value.This in fact represents the worst case scenario since α=0 means {squareroot over (1+3 cos²α)}=2, while α=π/2 means {square root over (1+3cos²α)}=1.

Hence for each of three field generators a bounded value for R, thevector distance of the sensor from that particular field generator, canbe calculated without any knowledge of the orientation α of the sensor.Since there are three field generators located at different knownpositions in the same plane (the x-y plane) and the distance R from eachof them to the sensor has been calculated, the x-y-z coordinates of thesensor can be determined from simple trigonometry. This positioningmethodology is shown schematically in FIG. 6. The three simulatedspheres of constant induced voltage centred on each of the three fieldgenerators, and bounded by the potential error in R, overlap at tworegions. One region is above the plane of the field generators and theother is below. In most applications, one solution is clearly erroneousand the location of the sensor can easily be uniquely determined.

At this stage the location of the sensor (but not its orientation) hasbeen calculated to a limited degree of accuracy. For some applicationsthis may be adequate, but in general the precise location and probablyorientation of the sensor are required. This is achieved by the use ofan iterative procedure in which the estimate of the x-y-z coordinates ofthe sensor, derived from the values of R for each of the three fieldgenerators, are used in the appropriate equation (4) for each of thenine generating coils to estimate values of θ and φ for the sensor, fromthese α is calculated for each of the three generators. Although θ and φcould be calculated from only two versions of equation (4), all nineversions are employed to improve the rate of convergence of the solutionand its immunity from noise. The three values of α can then be invokedin the appropriate equation (11) for each field generator to calculatein improved estimate for R for each of the generators. This process isrepeated, progressively reducing the error in R and α for eachgenerating until the desired level of accuracy is achieved. It should benoted that this technique avoids the problems of non-convergence whichwould arise if equation (4) were utilised directly because a goodestimate for R has been found before equation (4) is employed, and theestimate for R is bounded as shown schematically in FIG. 6.

In summary, and with reference to FIG. 7, the algorithm utilised by thecontroller 6 is as follows:

1. Assume α=0 initially. Thus ensures an over-estimate of R whichguarantees an intersection of the radial distances from the threegenerator.

2. Measure the voltages induced in the sensor by each of the 9individual generator coils, and then compute {square root over (V_(sDx)²+V_(sDy) ²+V_(sDz) ²)} for each of the three generators.

3. Invoke α in (11) and compute R for each of the three generators.

4. Compute the x-y-z coordinates of the sensor from the three values ofR.

5. Invoke these coordinates in the appropriate version of equation (4)for each of the nine generating coils and compute an improved estimateof θ and φ. This can be achieved by the use of, for example, theGauss-Newton Least Squares optimisation technique.

6. Use the improved estimates of θ and φ to calculate α for eachgenerator.

7. Return to step 3 until the difference between the new and previousestimates of α reaches a sufficiently low value commensurate with therequired positional accuracy in the x-y-z coordinates being achieved.

FIG. 8 depicts schematically the three spheres of constant inducedvoltage when the errors in R have been reduced to allow the location ofthe sensor to be determined uniquely. The technique employed thusguarantees convergence to a unique location, with a precision that canbe chosen in accordance with the requirements of the application.Indeed, it should be noted that in applications where the sensor ismoving within the magnetic field, the number of iterations can be chosendynamically for each calculation of the location of the sensor, therebyimproving the efficiency of the process. For example, the firstplacement of the sensor typically requires 10 iterations before thesolution is considered to have converged: this is considered to be sowhen the mean-square difference between the present and previous valuesof α is less than 10⁻⁶. Even with rapid movements of the sensor, it isunlikely that its angle α will change markedly from one positionalplacement to the next. By using the final value of α arrived at duringthe first placement as the initial estimate in the second placement, thenumber of iterations required to achieve the same convergence issignificantly reduced. And so on for all subsequent placements.Experiments have shown that as few as 3-5 iterations are required forconvergence after the initial placement.

Although the algorithm described above with reference to FIG. 7 ensuresconvergence to a unique location, allows both the location andorientation of a single coil sensor to be determined, and has proved tobe robust even in the presence of noisy signals from the sensor coil 7,a second, alternative algorithm has been developed which has furtheradvantages.

The first algorithm requires, at step 5, the solution of ninesimultaneous equations relating θ and φ for each of the field generatorsto the estimate of the x, y and z coordinates of the sensor. Thiscalculation can, dependent on the processing power of the controller 6,be time consuming, hence a second algorithm which is lesscomputationally intensive has been developed. This algorithm enables thelocation and orientation of the sensor 7 to be determined more rapidly.The second algorithm is based on the realisation that mathematically thevoltages induced in the sensor 7 by each set of three generating coils 3comprising each generator can be treated as vector quantities. Thismathematical treatment enables an angle ψ between the magnetic fieldlines and the direction vector of the sensor from a generator to becalculated. Once the values of ψ for each generator have been foundthere is no need to employ equation (4) since the values of α can becalculated directly from the values of ψ given a knowledge of the formof the magnetic field. Since nine versions of equation (4) need nolonger be solved this algorithm is computationally less intensive thanthe algorithm of FIG. 7.

The second algorithm will now be described in greater detail. In orderto explain the algorithm clearly and to demonstrate the mathematicalinsight on which it is based, the roles of the generating coils 3 andsensor coil 7 will be reversed i. e. for the purpose of the calculationthe single axis field sensor 7 will be replaced by a continuouslyenergised single axis field generating coil and the three orthogonalthree-axis field generators will be replaced by three orthogonalthree-axis field sensors. This is shown in FIG. 9. Although it should bestressed that the reversal of roles here is simply for the purpose ofmathematical elegance, this reversed configuration will in practice befeasible and in some position location applications may be desirable.

Referring now to FIG. 9, let the vectors joining each three-axis sensor(10) to the single axis generator (11) be R₁, R₂ and R₃ and let theangles between these vectors and the generator be α₁, α₂ and α₃. Thefield produced by the single axis generator (11) will pass through eachthree-axis sensor (10), and the magnitude and direction of the field maybe determined by processing the signals produced by each of the threeorthogonal sensor coils (12), forming each three-axis sensor (10), inresponse to the field. Let the signals in each of the three-axis sensor(10) be represented by the vector quantities V₁, V₂ and V₃, where eachcomponent of the vectors corresponds to the signal in each of theorthogonal sensing coils (12). Let the angle between the field at eachthree-axis sensor (10) and the vectors R₁, R₂ and R₃ be ψ₁, ψ₂ and ψ₃respectively, as shown in FIG. 10.

For the first estimate of the position of the generator 11, theorientation of the generator (11) is unknown, and α₁, α₂ and α₂ areassumed to be zero. The magnitude of the vectors R₁, and R₂ and R₃ arethen calculated from equation (11). As for the first algorithm, becauseof the nature of equation (11) a bounded value for the distance of thegenerator (11) from each of the three-axis sensors (10) is found and theoverlap of these bounded values can be used to give an initial estimateof the x, y and z components of each of the vectors R₁, R₂ and R₃.

The angles ψ₁, ψ₂ and ψ₃ are then calculated using the dot product, asfollows:

V_(n) , R_(n) =|V_(n) ||R_(n) | cosψ_(n)

${\cos \quad \psi_{n}} = \frac{\underset{\_}{V_{n}} \cdot \underset{\_}{R_{n}}}{{\underset{\_}{V_{n}}}\quad {\underset{\_}{R_{n}}}}$

Having found ψ_(n), we need to find α_(n) to improve the estimate ofposition. Referring to FIG. 11 ψ is the known angle and α is therequired angle. d represents the calculated distance from the generatorto the sensor.

Since the generator is a simple dipole, the field at the sensor is givenfrom equations (A-1) and (A-2) by:$B_{d} = {( \frac{2k}{d^{3}} )\quad \cos \quad \alpha}$$B_{\alpha} = {( \frac{k}{d^{3}} )\quad \sin \quad \alpha}$

The angle of the field at the sensor is given by:${\tan \quad \psi} = {\frac{- B_{\alpha}}{B_{d}} = {{- \frac{1}{2}}\quad \tan \quad \alpha}}$

and so α is obtained from ψ using:

tanα_(n)=−2 tanψ_(n)

Having found a new estimate for α_(n), a new estimate of the generatorposition is calculated using equation (11). The process is repeateduntil the position converges to the required degree of accuracy.

Once the position of the generator (11) has been determined in terms ofR _(n) and α_(n) the orientation of the generator may be calculated interms of θ and φ as follows.

Let U be a unit vector defining the orientation of the generatorrelative to the sensors. Using the dot product, we can set up threeequations to determine the three unknowns in U.

R₁ , U=|R₁ ||U|cosα₁=|R₁ |cosα₁

R₂ , U=|R₂ ||U|cosα₂=|R₂ |cosα₂

R₃ , U=|R₃ ||U|cosα₃=|R₃ |cosα₃

These linear equations are solved to find U, and then the orientation interms of θ and φ is given by:$\theta = {\arctan \quad ( \frac{\sqrt{U_{x}^{2} + U_{y}^{2}}}{U_{z}} )}$$\varphi = {\arctan \quad ( \frac{U_{x}}{U_{y}} )}$

(note that a four quadrant arctan function should be used).

Although the formulation of the second algorithm has thus far been forthe case of a single axis generator and multiple axis sensors thealgorithm can be applied to the case of a single axis sensor andmultiple axis generators. The only modification required between the twocases is the method by which the raw data for the algorithm (i. e. thevoltages induced) is acquired. The equations developed above aredirectly applicable to the single axis sensor multiple axis generatorcase since the magnetic coupling between two coils is the sameirrespective of which of the two coils is being driven.

The steps to be followed when employing the algorithm for the singleaxis sensor and multiple axis generator case will now be summarised:

1. Sequentially energise each of the three generator coils in each ofthe three generators 1 and measure the voltage induced in the sensorcoil 7 by each generator coil i. e. measure V_(1x), V_(1y), V_(1z),V_(2x), V_(2y), V_(2z), V_(3x), V_(3y), V_(3z).

2. Invoke α_(n) in equation (11) and compute |R_(n)| for each of thegenerator 1, 2 and 3. (for initial estimate set α=0).

3. From the intersection of three spheres of radius |R_(n)| calculatethe vector quantities R₁, R₂ and R₃.

4. Taking the three voltages induced in the sensor coil 7 by a singlegenerator 1 as a vector quantity e. g. V ₁=V_(1x) x+V_(zy) v+V_(1z) zcalculate the angle of the field ψ_(n) from the dot product V_(n),R_(n).

5. Calculate the angles α_(n) between the vectors R _(n) and the sensoraxis from ψ_(n) and equations A-1 and A-2.

6. Repeat steps 2 to 5 until the desired level of positioning accuracyhas been achieved.

7. Use final values of α_(n) and R _(n) to calculate the orientation ofthe sensor coil in terms of θ and φ.

It has been found that use of the second algorithm can improve the speedwith which the location and orientation of a sensor is determined by afactor of approximately 15 compared to the first algorithm.

For both algorithms the location and orientation of more than one sensorcan be determined without the need to replicate the field generators 1and amplifier 5. The field generated by any one field generating coil ismeasured at each of the sensors and the location and orientation of thesensors are simultaneous and independently calculated. The positions ofthe sensors may of course all be displayed on a single display unit 9.

The simple, small sensor used in this embodiment means that it canprovide position location in many situations where there is insufficientspace for the three coil orthogonal sensor used in prior art positionlocation systems. A particular field of application is the medicalfield, where access through body vessels is required, for example inendoscopy or non-invasive cardiovascular heart surgery. In these medialsituations the present location system may replace the use of x-rayimaging (fluoroscopy), giving considerable advantages in cost andeliminating x-ray exposure to both patients and medical staff. The lowfrequency magnetic fields used by the present system render the humanbody transparent, while the use of low field strengths ensues the systemis intrinsically safe.

During endoscopy it is desirable to know the path of the endoscopethrough the body. This may be achieved using the present location systemin three ways. Firstly, the single sensing coil may be pulled along thebiopsy tube and its position at regular intervals along the tube storedand displayed to provide a 3D map of the path. Secondly, a tubecontaining approximately a dozen single coil sensors may be placed inthe biopsy tube of the endoscope and the location of each of the sensorsdetermined. This would be a retro-fit to existing endoscopes.Alternatively, the single coil sensors may be placed in the wall of theendoscope during manufacture. In the second two cases a real timepicture of the path of the endoscope would be available at all times tothe endoscopist.

The present positioning system has been utilised in clinic field trialsto image in three dimensions the total configuration of a colonoscopewithin the human abdomen. A sensor according to the present inventionwas placed inside the biopsy channel of an endoscope.

The small inner diameter of the biopsy channel, typically 3.7 mm for acolonoscope, not only dictates that the sensor be of vanishingly smalldiameter, but also that it may only comprise a single coil, typically 1cm in length, orientated along the axis of the instrument. Thealgorithms of the present positioning system processes the signals fromthis sensor in such a way as to calculate the position of the sensorwithin the biopsy channel independent of its orientation. Suchindependence is crucial in colonoscopy since the sensor may adopt anyorientation for a single x-y-z location.

The positioning algorithm resides as software within an IBM 486 personalcomputer which, upon processing the information taken from the sensor atnumerous discrete positions along the biopsy channel, then displays thepath followed by the sensor as a continuous line on the monitor. Clearlythis path corresponds precisely to that of the endoscope. Moreover,because the information from the sensor at each location relates tothree dimensions, the imaged path on the monitor is likewise displayedin three dimensions. Visually the system achieves this by the use of“grey scale” colour coding whereby portions of the path further from theviewer (i. e. down into the screen) appear in darker shades of grey thanthe “under” portion. This features is unique among all conventionalimaging techniques for colonoscopy and represents a major advance in thefield.

To display the path of the endoscope, the endoscopist first passes thesensor down the biopsy channel until it reaches the tip of theendoscope. For convenience we have encapsulated the sensor within ahollow tubular catheter of the type used routinely with endoscopes. Thecatheter is then withdrawn at a uniform speed (although this is notcritical) while the system repeatedly determines the position of thesensor at discrete instances during its motion. During withdrawal thepath of the instrument is displayed on the monitor in three dimensions.In many situations a total image of the endoscope is not required, inwhich case the sensor need only be withdrawn along that portion of theinstrument of interest. To cater for patients lying in a variety ofpositions, perhaps changing during the investigation, the image may berotated in any direction. This is particularly advantageous inestablishing the radius of curvature of any bend in the endoscope thathappens to lie along the viewing axis. For example, a bend that is infact gradual, and hence poses no concern, can appear abrupt if viewedfrom some directions. A useful zoom facility on the image is alsoprovided. When the system is in normal use, the system display wouldideally be sited next to a standard camera monitor used to display theview from the endoscope. In this way the endoscopist is convenientlypresented with the path of the instrument in three dimensions on onedisplay, and the internal view from the endoscope optics on the other.

Initial validation of the system was performed with the aid of a rigidplastic framework to hold the endoscope in one of a number of predefinedconfigurations. X-ray imaging and the present magnetic field system wereapplied to seven different configurations of the endoscope. Theseincluded a sigmoid loop, an alpha loop, a reverse alpha loop, a gammaloop, and an “N” loop. The results, three of which can be seen in FIG.12 showed close agreement between the image produced by the presentpositioning system (shown on the left) and the X-ray image (shown on theright) in each case. The nature of the overlapping portions of thecolonoscope can be clearly seen from the images produced by the presentpositioning system. Some distortion of the images was caused by themetallic construction of the colonoscope perturbing the magnetic fields.However, this was minimal and the colonoscope configuration is clearlyevident from the images.

The clinical trails involved three patients undergoing colonoscopy for anumber of different indications. Ethical approval was obtained, as waswritten consent. The patients were sedated with a combination ofpethidine and midazolam before the examination. The colonoscope used wasa Pentax type FC38LH.

For the majority of each examination, the sensor was fully inserted intothe biopsy channel, and the display was configured to show the progressof the tip of the endoscope in real time. When progress becamedifficult, the sensor was withdrawn, which immediately produced an imageon the screen of the total path of the endoscope. With the aid of thisimage the removal of loops was straightforward, by using clockwise oranti-clockwise twist and simultaneous withdrawal of the endoscope.Similarly, when re-inserting the instrument the reformation of loops wasprevented by a combination of abdominal pressure and torque. Whereabdominal pressure was required the sensor was positioned in the loop,so enabling the endoscopist to see, by referring to the displayed image,whether pressure was being applied in the desired direction and to thecorrect extent. In each case examination around to the caecum wasachieved (i.e. total colonoscopy) and the procedure was tolerated wellby the patients. During the examinations, X-ray pictures were taken forcomparison against those obtained with the magnetic system. Two ofthese, a plan and side view, are shown in FIG. 13 together with thecorresponding image from the magnetic system. Agreement between the twois very close, the deviation being largely attributable to patientmovement between the two exposures.

The system has been shown to image the configuration of the endoscopewithin the patient's abdomen with close agreement to the X-ray image.The three dimensionality of the image has proven to be of great help indeciding the strategy for removing loops which form in the path of theendoscope during intubation. Indeed, this improvement in visualisationis likely to be of great benefit in teaching colonoscopy, as well asenabling experienced endoscopists to improve their technique when facingdifficult cases. The intrinsically safe nature of the system allows itto be in continuous use throughout the examination, presenting theendoscopist with as many images as the circumstances require. Thiscontrasts markedly with fluoroscopy which can only offer imagesintermittently and carries an exposure time limit for reasons of patientsafety, and X-ray pictures which are essentially only a “one-shot”option. Moreover, protective clothing need not be worn by any of thosepresent at the examination while the system is in use, nor is itnecessary for the examination room to be in any way specially prepared.Indeed, the system frees such examinations from having to take place ina room apart from the ward. If need be such examinations could becarried out in complete safety and with no loss in overall integrity, atthe patient's own bed in the ward.

A number of medical studies have considered the efficacy of colonoscopyas a screening methodology in asymptomatic subjects and have shown asignificant detection rate for adenomas and carcinoma in subjects overthe age of 60. Of particular note here is that some 50% of lesions wereproximal to the splenic flexure, hence the importance of performing atotal colonoscopy in such cases. The ability to conduct totalcolonoscopes routinely and efficiently is therefore an importantobjective. On the other hand it must be remembered that colonoscopy(total or otherwise) is associated with a certain morbidity andmortality due to the need to apply mechanical stress during intubationor withdrawal. The overall improvement in visualisation that the presentsystem affords, particularly it's three dimensionality, should bothraise the efficacy of total colonoscopy and reduce the risk ofperforation. This in turn may also help to reduce the dosage ofanalgesic and sedative drugs required.

Although the application of the present positioning system tocolonoscopy has been specifically addressed, the scope of the medicalapplications extends far beyond this by virtue of the very small size ofthe sensor(s). For example, bronchoscopy, gastroscopy and proceduresinvolving a nasogastric or endotracheal tube could all utilise thesensor described herein its present catheter form. Numerous othermedical applications requiring position or orientation information couldbenefit from either a single or multiple sensor implementation of thesystem.

Data gloves which facilitate the location of a wearer's hands, are usedin both medical and virtual reality applications. They enable theposition and direction of each of the fingers to be determined. Theprior art magnetic field location system using a three coil orthogonalsensor is clearly not applicable, so current data gloves use fibre opticstrain gauges. These require calibration every 2-3 minutes. The abilityto locate single coil sensors means that the sensors may be wound aroundeach joint of each finger giving a system which is less bulky, moreaccurate and only requires calibration during the manufacture of thegloves. FIG. 15 illustrates an exemplary data glove with sensor coilswound around each finger.

A particular area of application for the present positioning systemcomprises that of the so called “man-machine interface”. There arenumerous situations in which a human operator needs to interact with amachine, or computer, normally comprising some form of display device,examples of such interactions are with a conventional personal computer,a video conferencing system, or a virtual reality environment in whichthe operators field of view is filled by the display device, which inthis case may be three dimensional. The present positioning systemallows an operator to wear small, single coil sensors about his body toenable his movements to be detected and interpreted by a machine withoutthe need for physical contact between the operator and the machine. Forexample the positioning system of the present invention could enable anoperator to interact with images on a television or computer screenwithout the use of a conventional keyboard, mouse or stylus. Theoperator could wear single coil sensors on his fingertips, for examplein thimbles, or a thin glove, the location and orientation of whichcould be detected within a magnetic field generated within the vicinityof the display screen. Linking the positioning system to the computingsystem would allow the computing system to have knowledge of theposition of the operators fingertips in three dimensions. A computerdrawn replica of the user's hand which precisely emulates the movementsof the user's own fingers, could then be utilized by the user tointeract with the computer system. Thus when the user makes handmovements the virtual hand on the screen can be made to grasp andmanipulate objects in the display, for example moving portions of text,rotating an engineering drawing, selecting an icon to activate asoftware program, etc. The virtual hand could also be used to controlwindows and menus and to draw diagrams. The advantage of such a manmachine interface is that its use is completely intuitive, requiring notraining.

Since the positioning system of the present invention enables theposition of a sensor to be located in three dimensions, the extension ofsuch a man machine interface to a three dimensional virtual realityenvironment is clearly possible. In this case the computer systeminvolved may need information regarding the position of other parts ofthe operator's body than his hands, for example the image displayed tothe operator may be dependent on the location and orientation of hishead, in which case small single coil sensors can clearly be worn forexample on each temple.

In a second embodiment the invention enables a sensor, comprising threeorthogonal sensing coils, to be located in three dimensions relative toa single field generator comprising three orthogonal generating coils.

With reference to FIG. 14, a field generator 1, comprising threegenerating coils 3, as previously described is mounted on a surface 2.Each generating coil is electrically connected to an amplifier 5 and isdriven as previously described.

The sensor 7 in this embodiment comprises three mutually orthogonalsensing coils, A, B and C, each of which is separately electricallyconnected to a measurement unit 8.

In use the three generating coils are sequentially energised aspreviously described, but when each coil is energised the voltagesinduced in each of the three sensing coils V_(A), V_(B) and V_(C) aremeasured by the measurement unit 8 and stored by the controller 6. Thecontroller 6 then calculates from these three voltages the location ofthe sensor 7 relative to the single field generator 1.

The controller is able to calculate the location of the sensor, eventhough the axes of the generated fields have not been directed towardsthe sensor, by employing an algorithm which weights the voltages inducedin the three sensing coils by a direction dependent weighting, and thenalters these weightings to achieve a calculated maximum field strengthat the sensor. In order to more fully describe this algorithm the fieldfrom a single small coil is first considered.

The magnetic field produced by a small coil, from equations (A-1) and(A-2), is given by: $\begin{matrix}{\underset{\_}{B} = {( \frac{k}{R^{3}} )\quad ( {{2\quad \underset{\_}{a}},{{\cos \quad \theta} + {{\underset{\_}{a}}_{\theta}\quad \sin \quad \theta}}} )}} & (12)\end{matrix}$

where R=distance from the coil

θ=angle from the axis of the coil

k=constant for coil (size, drive current, no. turns etc).

a_(R) is a unit vector in the direction of B_(R) (see Appendix A—FIG.A-1)

a_(θ) is a unit vector in the direction of B_(θ) (see Appendix A—FIG.A-1)

Now, the magnitude of the magnetic field $\begin{matrix}{{\underset{\_}{B}} = {\frac{k}{R^{3}}\quad \sqrt{{3\quad \cos^{2}\quad \theta} + 1}}} & (13)\end{matrix}$

and so it can be seen that for a given distance from the coil, the fieldstrength is greatest when θ=0 i.e. on the axis of the coil. Clearly, ifthe effective axis of the coil could be directed towards the sensor, thesensor would experience a maximum in field strength.

In order to steer the effective axis of the coil without physicallymoving it, additional coils are required. To steer the effective axisover 3D, three coils are required in total. Assuming three mutuallyperpendicular coils D_(x), D_(y), D_(z) lying along each of thecartesian axes x, y and z, each coil being centred on the origin, bysetting the currents to each coil as:

I_(x)=I cos θ cos φ

I_(y)=I cos θ sin φ

I_(z)=I sin θ

the effective axis of the resulting field may be steered withoutchanging the magnitude of the field. φ is the angle anticlockwise from xin the xy plane, and θ is the elevation towards the z axis.

Assuming the notation of FIG. 2, OP represents the effective axis of thefield. That is a single drive coil, centred on the origin, with its axisalong OP, fed with current I, would create the same field as the threecoil arrangement with the currents I_(x), I_(y) and I_(z) as described.

Thus if the field strength at the point we wished to locate could bemeasured, we would find that when axis OP pointed at this point, thefield strength would be a maximum.

The field strength is measured using 3 orthogonal sense coils, centredon a single point. In this case an AC field must be used in the drivecoils. Let the sensor coils be A, B and C, and let the amplitude of thevoltages induced be V_(A), V_(B) and V_(C). The field strength can becomputed from

B=k _(s) (V _(A) ² +V _(B) ² +V _(C) ²)

where k_(s)=a constant for the sensor and frequency used.

The effective axis of the resulting field, could be physically steeredtowards the sensor, and V_(A), V_(B), V_(C) monitored to maximise B.However this is difficult in practice to achieve since both θ and φwould need to be simultaneously altered while measurements from thesensor are taken. This leads to slow position location, and limits thesystem to locating a single sensor. The approach adopted in thisembodiment is as follows. The drive currents for all the coils are setto I, and not to the values which would be required to physically steerthe effective field axis, as discussed above.

i.e.

I_(x)=I

I_(y)=I

I_(z)=I

Effectively steering of the field axis is carried out AFTER the fieldmeasurements have been made by weighting or scaling these measurementsby direction dependent weighting factors. Thus, instead of physicallyaltering θ, φ and then measuring B, the following technique is used.

1. Switch on D_(x), with I_(x)=I

2. Measure V_(ADx), V_(BDx), V_(CDx)

3. Switch off D_(x); Switch on D_(y), with I_(y)=I

4. Measure V_(ADy), V_(BDy), V_(CDy)

5. Switch off D_(y); Switch on D_(z), with I_(z)=I

6. Measure V_(ADz), V_(BDz), V_(CDz)

7. Switch off D_(z)

For the physically steered field: I_(x)=I cos θ cos φ, rather than I.The same result is achieved by weighting the results from step 3 by cosθ cos φ. The same logic applies to the remaining results, using therelevant weighting factor.

Thus:

B ² =K _(s) ²((V _(ADx) cos φ+V _(ADy) sin φ) cos θ+V _(ADz) sin θ)²

+((V _(BDx) cos φ+V _(BDy) sin φ) cos θ+V _(BDz) sin θ)²

+((V _(CDx) cos φ+V _(CDy) sin φ) cos θ+V _(CDz) sin θ)²

Note that the “signs” of the amplitude are important e.g.

phase shift=0=−ve

phase shift=π=−ve

In this expression for B², θ and φ are the only variables.

In order to find the values of θ and φ which give the maximum B², theGauss-Newton optimisation technique is used. This copes well with sum ofsquares type expressions. The expression for B² is well behaved, andonly a few iterations are required.

In order to find the precise location of the sensor we must now find R.

If we square and sum the field magnitudes at the sensor for eachgenerator coil, we find that:${{{\underset{\_}{B}}_{0x}}^{2} + {{\underset{\_}{B}}_{0y}}^{2} - {{\underset{\_}{B}}_{0z}}^{2}} = {6\quad ( \frac{k_{1}}{R^{3}} )^{2}}$

and so R may be found from:$R^{3} = {k_{2}\quad \sqrt{\frac{6}{{{\underset{\_}{B}}_{0x}}^{2} + {{\underset{\_}{B}}_{0y}}^{2} + {{\underset{\_}{B}}_{0z}}^{2}}}}$

The cartesian coordinates of the sensor are then

x=R cos θ cos φ

y=R cos θ sin φ

z=R sin θ

As with the first embodiment the location of multiple sensors isfacilitated because the generating coils are only energised sequentiallyallowing the generated field to be simultaneous measured at any numberof locations.

Although in both embodiments of the invention described herein thevoltages induced in the sensor coil 7 by the generating coils 3 aredistinguished one from the other by employing a time multiplexingapproach, i.e. the generating coils are energised sequentially, afrequency multiplexing approach may also be adopted within the scope ofthe present invention. For example in such an approach each generatorcoil 3 could be driven at a different frequency so that a plurality ofgenerating coils 3 could be simultaneously energised while stillallowing the voltage induced in the sensor 7 by each generating coil tobe distinguished by its frequency. In such an arrangement the sensorwould need to be responsive to all the energising frequencies and someform of frequency filtering would need to be provided. This filteringcould be provided by discrete physical bandpass filters electricallyconnected to the sensor 7, or, if an A to D converter is employed asdescribed herein, filtering of the signal from the sensor 7 can beaccomplished by signal processing software in the controller 6. The useof frequency multiplexing to acquire the data for position determinationcan significantly increase the operating speed of the positioning systemsince measurements from generating coils can be taken simultaneously.Disadvantages of such a frequency multiplexing system are that it ismore complex than a time multiplexed system and requires greaterelectrical bandwidth. A combination of time and frequency multiplexingcould of course be used.

In both embodiments it is desirable that the quasi-static magnetic fieldgenerated by a coil is established quickly and is allowed to decayquickly. For this reason it is preferred to use a first order ratherthan a second order drive circuit. For the generating coils employed thefield settles within one cycle of being switched on.

It will be appreciated that alternative configurations of bothembodiments for different applications, for example locating a sensorwithin a two dimensional plane, are envisaged within the scope of thepresent invention.

As will be clear to one skilled in this art, the roles of the generatingand sensing coils may be reversed while still benefitting from theadvantages of the present invention. That is the sensing coil or coilsmay be used as field generating elements, and the generating coils maybe used as field sensing elements.

This reversal of roles has particular advantage where a static field,such as that generated by a bar magnet is employed according to thefirst aspect of the invention, since such a field generating elementmust be effectively permanently “energised”. The reversal of rolesallows the “sensor” permanently to generate a field which is sensed ateach of the “generating elements” and the location and orientation ofthe “sensor” is then determined as before.

Consider a current, I, flowing through a small planar coil of radius, b,(FIG. 16). The frequency of I is chosen to be sufficiently low such thatstatic field distributions apply.

For a point P in the field whose distance R from the coil is such thatR>>b, it is readily shown for example in D K Cheng, Field and WaveElectromagnetics, 2nd Ed, Addison Wesley, 1989, that $\begin{matrix}{{B_{R} = {\frac{2\quad k_{c}\quad \cos \quad \theta}{R^{3}}\quad {and}}},} & \text{(A-1)} \\{B_{\theta} = \frac{k_{c}\quad \sin \quad \theta}{R^{3}}} & \text{(A-2)}\end{matrix}$

where k_(c) is a known function of I and b. B_(R) and B_(θ) representthe vector components of the magnetic flux density at point P resolvedalong axes parallel to the line R and the angle θ. Note that, byconvention, θ is measured from the axis of the coil.

In order to remove the magnetic flux density at P onto a 3-dimensionalextension coordinate system, consider first the coil in the y-z plane,centered on the origin (FIG. 17).

If point P is distance x from the coil (i.e. origin) along the x-axis,and its vector distance is R, the distance in the y-z plane byPythagoras is {square root over (R²−x²)}. Since R²=x²+y²+z², thisdistance reduces to {square root over (y²+z²)}, as shown. It thenfollows that, $\begin{matrix}{{{\sin \quad \theta} = {\frac{\sqrt{y^{2} + z^{2}}}{R}\quad {and}}},} & \text{(A-3)} \\{{\cos \quad \theta} = \frac{x}{R}} & \text{(A-4)}\end{matrix}$

Resolving the magnetic flux density at P onto a cartesian system gives,for the x-axis component.

B _(x) =B _(R) cos θ−B _(θ) sin θ

From (A-1) and (A-2) this becomes,$B_{x} = {\frac{k_{c}}{R^{3}}\quad ( {{2\quad \cos^{2}\quad \theta} - {\sin^{2}\quad \theta}} )}$

and from (A-3) and (A-4), $\begin{matrix}{B_{x} = {\frac{k_{c}}{R^{5}}\quad ( {{2x^{2}} - y^{2} - z^{2}} )}} & \text{(A-5)}\end{matrix}$

Resolving similarly onto the y-z plane gives.

B _(yz) =B _(R) sin φ+B _(θ) cos φ

which from (A-1) and (A-2) becomes,$B_{yz} = {\frac{k_{c}}{R^{3}}\quad ( {3\quad \cos \quad \theta \quad \sin \quad \theta} )}$

and from (A-3) and (A-4), $\begin{matrix}{B_{yz} = {\frac{k_{c}}{R^{5}}\quad ( {3x\quad \sqrt{y^{2} + z^{2}}} )}} & \text{(A-6)}\end{matrix}$

Resolving the magnetic flux density at P into its y and z components(FIG. 18) gives,$B_{y} = {{B_{yz}\quad \cos \quad \varphi} = {B_{yz}\quad ( \frac{y}{\sqrt{y^{2} + z^{2}}} )}}$

${and},{B_{z} = {{B_{yz}\quad \sin \quad \varphi} = {B_{yz}\quad ( \frac{z}{\sqrt{y^{2} + z^{2}}} )}}}$

From (A-6) these become, $\begin{matrix}{{B_{y} = {\frac{k_{c}}{R^{5}}\quad ( {3{xy}} )\quad {and}}},} & \text{(A-7)} \\{B_{z} = {\frac{k_{c}}{R^{5}}\quad ( {3{xz}} )}} & \text{(A-8)}\end{matrix}$

For a coil (dipole) in the y-z plane, equations (A-5), (A-7) and (A-8)fully describe the resolved cartesian components of the magnetic fluxdensity at a point P located at a radial distance R from the coil. Thecorresponding equations for coils in the x-y and x-z planes can bedeveloped in an identical manner. The complete set of formulae cantherefore be summarised thus.

For a coil in the y-z plane: $\begin{matrix}{B_{x} = {\frac{k_{c}}{R^{5}}\quad ( {{2x^{2}} - y^{2} - z^{2}} )}} & \text{(A-9)} \\{B_{y} = {\frac{k_{c}}{R^{5}}\quad ( {3{xy}} )}} & \text{(A-10)} \\{B_{z} = {\frac{k_{c}}{R^{5}}\quad ( {3{xz}} )}} & \text{(A-11)}\end{matrix}$

For a coil in the x-y plane: $\begin{matrix}{B_{x} = {\frac{k_{c}}{R^{5}}\quad ( {3{xz}} )}} & \text{(A-12)} \\{B_{y} = {\frac{k_{c}}{R^{5}}\quad ( {3{yz}} )}} & \text{(A-13)} \\{B_{z} = {\frac{k_{c}}{R^{5}}\quad ( {{2z^{2}} - x^{2} - y^{2}} )}} & \text{(A-14)}\end{matrix}$

For a coil in the x-z plane: $\begin{matrix}{B_{x} = {\frac{k_{c}}{R^{5}}\quad ( {3{xy}} )}} & \text{(A-15)} \\{B_{y} = {\frac{k_{c}}{R^{5}}\quad ( {{2y^{2}} - x^{2} - z^{2}} )}} & \text{(A-16)} \\{B_{z} = {\frac{k_{c}}{R^{5}}\quad ( {3{yz}} )}} & \text{(A-17)}\end{matrix}$

What is claimed is:
 1. A method of making a three-dimensional map of astructure internal to an anatomical body, the method comprising: a)moving a magnetic field sensor to a position within the anatomical body;b) generating, external to the anatomical body, magnetic radiation froma first magnetic field source positioned at a first fixed and knownlocation on a plane surface; c) generating, external to the anatomicalbody, magnetic radiation from a second magnetic field source positionedat a second fixed and known location on the plane surface; d)generating, external to the anatomical body, magnetic radiation from athird magnetic field source positioned at a third fixed and knownlocation on the plane surface; e) detecting with the sensor within theanatomical body, magnetic field information from each of the magneticfield sources located on the plane surface; f) ascertaining a locationof the sensor based upon the magnetic field information detected by thesensor; g) storing data indicative of the ascertained location of thesensor; h) moving the magnetic field sensor to another position withinthe anatomical body; i) repeating steps a-h until sufficient data isstored to form a three-dimensional map corresponding to movement of thesensor within the anatomical body; and j) displaying a three-dimensionalmap formed based on the stored data.
 2. The method of claim 1, whereinthe magnetic field sensor is a single coil sensor.
 3. The method ofclaim 1, wherein the magnetic field sensor includes multiple coilwindings, and wherein all of the multiple coil windings are wound abouta common axis.
 4. The method of claim 1, wherein magnetic field sensorincludes multiple coil windings, and wherein all of the multiple coilwindings are wound about a common core.
 5. The method of claim 1,wherein each magnetic field is generated using a plurality of fieldgenerating coil windings.
 6. The method of claim 1, wherein each fixedand known location surrounds a coil-free region.
 7. The method of claim1, wherein each field is sequentially detected by the sensor.
 8. Themethod of claim 1, wherein each field is simultaneously detected by thesensor.
 9. The method of claim 1, wherein the three-dimensional mapreflects contours of an anatomical structure.
 10. The method of claim 1,wherein the three-dimensional map is displayed on a two-dimensionalmonitor using color coding.
 11. The method of claim 1, wherein thesensor is connected to a medical instrument and is moved within theanatomical body together with the medical instrument.
 12. The method ofclaim 1, further including simultaneously displaying an actual image ofthe internal structure with the three-dimensional map.
 13. A method ofmaking a map of a structure internal to an anatomical body, the methodcomprising: a) moving a magnetic field sensor to a position within theanatomical body; b) generating, external to the anatomical body,magnetic radiation from a magnetic field source positioned at a fixedand known location; c) detecting with the sensor within the anatomicalbody, magnetic field information from the magnetic field source; d)ascertaining a three-dimensional location of the sensor relative to themagnetic field source as a function of the magnetic field detected bythe sensor; e) storing three-dimensional location data indicative of theascertained location of the sensor relative to the magnetic fieldsource; f) moving the sensor to another position within the anatomicalbody; g) repeating steps b-f until sufficient three-dimensional locationdata is stored to form a three-dimensional map corresponding to movementof the sensor relative to the magnetic field source within theanatomical body; and h) displaying a three-dimensional map of thelocations of the sensor relative to the magnetic field source that isformed based on the stored data.
 14. The method of claim 13 wherein themagnetic field sensor is a single coil sensor.
 15. The method of claim13, wherein the magnetic field sensor includes a plurality of coils. 16.A method of making a three-dimensional map of a structure internal to ananatomical body, the method comprising: a) moving a magnetic fieldsensor to a position within the anatomical body that is formed fromthree mutually orthogonal sensing coils positioned about a commonorigin; b) generating, from a known location external to the anatomicalbody, a plurality of magnetic fields from three mutually orthogonalgenerating coils positioned about a common origin; c) detecting, withthe three coil sensor within the anatomical body, the plurality ofmagnetic fields from the three mutually orthogonal generating coils; d)ascertaining a location of the three coil sensor as a function of theplurality of magnetic fields detected by the sensor; e) storing dataindicative of the ascertained location of the three coil sensor; f)moving the three coil sensor to another position within the anatomicalbody; g) repeating steps b-f until sufficient data is stored to form athree-dimensional map; and h) displaying a three-dimensional map formedbased on the stored data.
 17. The method of claim 16, wherein each ofthe magnetic fields is sequentially detected by the three coil sensor.18. The method of claim 16, wherein multiple magnetic fields aresimultaneously detected by the three coil sensor.